Designing Robust Linear Output Feedback Controller based on CLF-CBF Framework

Core Concepts

Synthesizing robust output feedback controllers for path planning in robotics.

Abstract

The content discusses the design of output feedback controllers for path planning in robotics, focusing on stability and safety using Control Lyapunov and Barrier Functions. It explores the integration of high-level path planning with low-level control processes to navigate through environments efficiently. The approach is tested in simulation environments under practical conditions like limited field of view measurements. I. Introduction: Path planning in mobile robotics focuses on finding trajectories while ensuring collision avoidance. Biological systems demonstrate flexible navigation capabilities without detailed maps. II. Notation and Preliminaries: Defines system dynamics, constraints, and relative degree concepts. III. Problem Setup: Synthesizes robust controllers for convex cells using linear programming. IV. Control With Limited Field of View: Discusses rescaling bearing measurements for controller design. V. Control With Bearing Measurements: Explores rescaling bearings to simulate full displacements for controller synthesis.

Stats

We propose two objectives for navigating in an environment: traversing by making loops or converging to a stabilization point smoothly between cells. The work integrates high-level path planning with low-level control processes to design robust output feedback controllers. The approach is tested under practical conditions like bearing-only measurements and limited field of view.

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Designing Robust Linear Output Feedback Controller based on CLF-CBF framework via Linear~Programming(LP-CLF-CBF)

by Mahroo Bahre... at arxiv.org 03-22-2024

https://arxiv.org/pdf/2403.14519.pdf

Deeper Inquiries

How can the proposed controller synthesis method be extended to handle non-linear systems

To extend the proposed controller synthesis method to handle non-linear systems, we can utilize techniques such as feedback linearization or nonlinear control methods. Feedback linearization transforms a nonlinear system into a linear one through a change of variables and feedback control law design. By introducing new state variables and designing appropriate feedback controllers based on these transformed states, we can effectively apply the controller synthesis method developed for linear systems to nonlinear ones. Additionally, techniques like Lyapunov-based control or adaptive control can be employed to ensure stability and performance in the presence of nonlinearity.

What are the implications of using only bearing measurements on the overall performance of the robot's navigation

Using only bearing measurements in robot navigation has several implications on overall performance. Firstly, relying solely on bearing measurements limits the information available for localization compared to full displacement measurements. This may lead to challenges in accurately estimating the robot's position relative to landmarks and obstacles in the environment. The lack of depth information from bearings could result in difficulties with obstacle avoidance and precise path planning, especially in complex environments with varying terrain or structures. Furthermore, bearing measurements are susceptible to noise and uncertainties that can affect the accuracy of navigation tasks. Limited field-of-view inherent in bearing sensors may also restrict visibility and coverage of landmarks within range, potentially leading to incomplete mapping or localization errors. However, despite these limitations, efficient algorithms for processing bearing data combined with robust control strategies can still enable effective navigation by leveraging available information optimally while compensating for measurement inaccuracies.

How can the concept of convex cell decomposition be applied to more complex environments beyond 2D spaces

The concept of convex cell decomposition applied in 2D spaces can be extended to more complex environments beyond 2D by generalizing it into higher dimensions (3D or higher). In three-dimensional spaces, convex polytopes become polyhedra where each face is itself a polygonal region bounded by straight edges forming planar surfaces. For instance: 3D Environments: Instead of cells being polygons as seen in 2D decompositions, they would now be polyhedrons defined by flat faces enclosing volumes. Higher-Dimensional Spaces: Extending further into higher dimensions involves defining convex regions using hyperplanes instead of planes found at lower dimensions. Algorithm Adaptation: Algorithms used for cell decomposition need modifications to handle additional dimensions while maintaining properties like connectivity between cells. Applications: Beyond robotics applications like drone navigation through complex terrains requiring volumetric representations rather than just surface-based divisions will benefit from this extension. By adapting convex cell decomposition principles appropriately across different spatial dimensions, it becomes possible to efficiently partition diverse environments facilitating path planning and navigation tasks effectively even outside traditional 2D scenarios.